Questions tagged [error-propagation]

Methods for calculating errors of a function whose arguments have individual errors.

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1answer
167 views

Accounting for uncertainty in a fit coefficient

So given some empirical data of $I_T$ vs $r$ I'd like to fit that to some model given by $$ I_T=\frac{I_0}{1+F \sin\bigg(\frac{2\pi d}{\lambda}\frac{f}{f^2+r^2}\bigg)} $$I am trying to analyze data ...
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16 views

Exact Corrections to Measured Data in a Paper?

http://fy.chalmers.se/~f7xiz/TIF080/pendulum.pdf I am really confused by this paper. They make corrections to the value of $g$ from theoretical corrections, but they plug in measured values with ...
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278 views

Parameter uncertainty in Least Squares fit to Vector Valued Function

Suppose I have to fit a vector field $\vec{y}_i$ with a vector valued function $\vec{f}_i = \vec{f}(\vec{x}_i; \vec{p})$, so both $\vec{y}_i, \vec{f}_i \in \mathbb{R}^m$, where $\vec{x}_i \in \mathbb{...
3
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1answer
1k views

Calculating the uncertainty on a ratio result in A/B test

If I am running an A/B test in which I have two randomly assigned groups of users and I am calculating a conversion on some action, how do I then calculate the uncertainty on the result? For example, ...
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1answer
39 views

Error Propagation and Error Partition

Given a a general form of a model $F$ ( which could be an explicit formula or set of formulas) with its input $x$ and output $y$. Suppose that the input $x$ has an error $\delta x$, so that given ...
10
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1answer
8k views

Linear model where the data has uncertainty, using R

Let's say I have data that has some uncertainty. For example: X Y 1 10±4 2 50±3 3 80±7 4 105±1 5 120±9 The nature of the uncertainty could be repeat ...
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60 views

Type B uncertainties and statistical analysis

In the Guide to Uncertainty in Measurement (GUM), two classes of methods to evaluate uncertainties are distinguished : a type A evaluation is a statistical method, applicable when a set of ...
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178 views

Uncertainties on fitted parameters in least squares circle fit

To fit a given a set of data points (x,y) to a circle, one can use a least squares fit and obtain values for the center of the circle (xc, yc) and the circle's radius (R). However, each of the data ...
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3k views

Line of best fit for data with error in x and y

I have a two dimensional dataset which comes from prior statistical analysis. Each point $(x_n,y_n)$ in the dataset has an error estimate $\sigma_{x,n}, \sigma_{y,n}$ for both coordinates. The $x_n$ ...
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92 views

Propagation of uncertainty through a correlation with its own uncertainty

So I'm trying to do propagation of uncertainty for the first time (read: I'm a noob at this), and it's proving to be a challenge. I'm trying to estimate the uncertainty in the friction factor of the ...
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26 views

Find error on the inputs

Suppose that we have a model with an input and an output. The model is exact (no structural uncertainty). However there is an error in the output ( the error is detected from already given exact ...
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2answers
1k views

Uncertainty in a fractional count

What is the uncertainty (68% confidence level) of $N/M$, where $N$ is the number of entries that pass a cut and $M$ is the total number of entries? ($N$ and $M$ are both integers, and I'm interested ...
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1answer
937 views

Propagate errors in measured points to Simpson's numerical integral

I have a set of measured/observed $y(x)$ points, each with an assigned standard deviation: $$y: \{y_0\pm\sigma_{y_0}, y_2\pm\sigma_{y_2}, ..., y_N\pm\sigma_{y_N}\}$$ I use scipy's implementation of ...
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579 views

error propagation on the median

Suppose to have a set of exact data $x_i, i=1,\dots,N$ and to calculate its median value $m$. Then, a sound way to estimate the error $\delta m$ on $m$ would be bootstrapping. (I think...) But what ...
3
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1answer
11k views

Calculating uncertainties for histogram bins of experimental data with known measurement errors

I have a set of experimental data (with each data-point having its own measured uncertainty), and I wish to produce a histogram of it. The x values of the edges of each bin are already defined. The ...
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148 views

How to mitigate the hierarchical error propagation in tree-structured classification

Suppose we have a multi-class classification problem, where the number of classes $K \geq 3$ We use a tree structure of multiple SVMs to divide and conquer the problem, with one example in the figure ...
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1answer
1k views

Estimate error of predicted value obtained by linear regression model

I have measured 2 parameters, r and p. Each parameter was measured in three technical replicates (n=3) per sample. r is measured directly. p is measured indirectly; the data obtained is output ...
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608 views

Error in Linear Regression Parameters: Using mean measurement vs. all measurements

I have a set of measurements y taken at 17 different values of x, with 50 repeated measurements at each value of x. They follow a simple linear relationship y = mx + c, and I am fitting the parameters ...
3
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1answer
351 views

Combining measurements with known uncertainties

I have $N$ rulers that each have a different but known level of accuracy, e.g. one's a meterstick, one's a yard stick, etc. I measure the length of my table using each ruler. How do I combine ...
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851 views

Error equation for distance between points in spherical coordinates

(Question brought over from here, after asking here) Consider two points with spherical coordinates: $a=(r_1,\theta_1,\phi_1)$ and $b=(r_2,\theta_2,\phi_2)$. The cartesian coordinates of the points ...
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1k views

uncertainties from Monte Carlo simulation and error propagation are different

Inspired by this post Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?, I try to check it myself using a simple function f=A/B, where A is 10 with uncertainty 1 and B ...
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2answers
1k views

Propagation of uncertainty through a linear system of equations, Ax=b, where A and b are correlated

I have a linear system of equations in the form Ax = b. The elements of A and b were experimentally determined and as such have some uncertainty. Within each row, A and b are correlated. Between rows, ...
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57 views

Confidence interval for the median - continued

I have a set of values $x_i\quad i=1,…,N$ of which I can calculate the median M. Each $x_i$ has an error $\delta x_i$. The $x_i$ values are the result of a maximum likelyhood estimation and their ...
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1answer
2k views

Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?

If I have a deterministic, analytic model, $y=f(x)$, I can analytically calculate the uncertainty in $y$ from a known uncertainty in $x$, $\sigma$. Or I can do a Monte Carlo integration: sample from ...
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1answer
501 views

Generalised linear models error distribution (continuous response)

I'm a bit confused about what error distribution I should use for the generalised linear models that I am running. My response variable is litter decay rate (k) (continuous, which runs from -1.5 to +1....
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152 views

Propagating uncertainties using random forest out-of-bag accuracy estimates

Let's say I train a random forest on some data and get an out-of-bag accuracy estimate of 90%. I then predict a quantity using this trained forest. What should be the uncertainty I give to that ...
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3answers
2k views

How to combine two measurements of the same quantity with different confidences in order to obtain a single value and confidence

Back in the lab at university, we were taught to measure the quantity of interest some number of times (call this N), and then calculate the standard error. The underlying assumption here is that you ...
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2answers
3k views

Adding Up Margins of Error

I'd like to add data from Census.gov, but I don't know how to add up the Margin of Error. Example, I have the estimate number of renters in Congressional District 1, (203,941 +/- 4,892) and the same ...
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210 views

Monte Carlo error propagation

Consider a set $X$ of $N$ iid random variables, each one with its own standard deviation: $$X: \{x_1\pm\sigma_1, x_2\pm\sigma_2, ..., x_N\pm\sigma_N\}$$ Say I have a "black box" numerical function ...
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2answers
8k views

Error propagation in a linear model

I am currently interested in learning more on error propagation. At the moment I am trying to find out how to calculate the uncertainty of a value that is obtained from a linear model. For the linear ...
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107 views

Do Monte Carlo perturbations capture all the uncertainty in prediction?

I have a model $M$ that I use to predict a value $y = M(\vec x)$. I have known one-$\sigma$ error bars on each input $x_i \in \vec x$. I want to know the one-$\sigma$ error bar on my prediction $y$. ...
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2answers
2k views

How to propagate uncertainty into the prediction of a neural network?

I have inputs $x_1\ldots x_n$ that have known $1\sigma$ uncertainties $\epsilon_1 \ldots \epsilon_n$. I am using them to predict outputs $y_1 \ldots y_m$ on a trained neural network. How can I obtain ...
3
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1answer
94 views

Propagate uncertainty of a parameter through a function

Suppose I have a probability distribution (in fact I've got a nice case where that distribution is Gaussian) on a parameter value. e.g. the parameter $x$ has $\mu = 3$ and $\sigma^2 = 1$. Now suppose ...
7
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3answers
18k views

Variance of an average of random variables

This seems like it should be a pretty common problem. I have four estimates of fishing effort, each with its own variance. For subsequent calculations, I want the mean of the four estimates, and a ...
1
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1answer
65 views

Are the parameters of Non-linear regression independent of each other?

I'm propagating error in the parameters determined by the following growth function... $$ \hat{y} = ae^\frac{t}{b} + (1- a)e^\frac{t}{c} $$ Say I have another model that uses the parameters {a,b,c} ...
4
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1answer
8k views

Backpropagation with Cross-entropy Cost Function

I'm using the cross-entropy cost function for backpropagation in a neutral network as it is discussed in neuralnetworksanddeeplearning.com. I got help on the cost function here: Cross-entropy cost ...
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2answers
36k views

Cross-entropy cost function in neural network

I'm looking at the cross-entropy cost function found in this tutorial: $$C = -\frac{1}{n} \sum_x [y \ln a+(1−y)\ln(1−a)]$$ What exactly are we summing over? It is, of course, over $x$, but $y$ and $a$ ...
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1answer
2k views

Error propagation and relative error

Say I have measured the value A = 50 +- 2 and from this I am calculating the value: B(A) = A^2 From what I understand I calculate the new error using error propagation to be delta_B = dB/...
2
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1answer
101 views

How to consider propagated measurement errors and "statistical errors"

I come from an Engineering background, and I am familiar with some basics of error treatment. However, discussing with a friend over some data he had to analyze, we couldn't quite figure out what to ...
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2k views

What is the correct way to combine data points with error?

If I have a 2-D data, say $y = f(x)$, with error in the dependent variable, $\delta y$ in this case, and I want to transform this data set to a coarser independent variable grid, $x$, what is the ...
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1k views

Adding numbers with asymmetric uncertainties

I need to add a series of numbers with asymmetric standard deviations, such as $$5_{-2}^{+1} \,+ \,3_{-3}^{+1}.$$ Although I know it's common to add the upper errors ($\sigma_{\scriptsize{+}}$) and ...
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0answers
128 views

Propagation of uncertainties in functions not continuously differentiable

According to the Guide to the Expression of Uncertainty in Measurement as published by the Bureau International des Poids et Mesures (BIPM), the combined standard uncertainty $u_c^2$ for a function $y ...
3
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1answer
373 views

Disadvantages of uncertainty in modeling

I am preparing a presentation, my work mainly concentrates on uncertainty and sensitivity analysis. I was wondering if I can convince my audience by the importance of studying uncertainty in modeling. ...
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0answers
148 views

Uncertainty of sum of values estimated through linear regression

I have a continuous record of a variable X, which I want to use as a surrogate for another system value Y. I have a number of measurements of Y, which I can plot against concurrent measurements of X ...
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1answer
68 views

Propagating RMSECV?

I have two regression models, each of which has an associated root mean squared error of cross validation (RMSECV). I would like to combine the results of the models using a weighted average to get a ...
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1answer
94 views

Backward propagation algorithm demonstration in neural networks: any VERY-SMALL-STEP by VERY-SMALL-STEP demonstration?

I'm looking for a VERY DETAILED demonstration for the backward propagation algorithm in neural networks machine learning. Specifically the step below. I've got the excellent Michael Nielsen ...
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0answers
222 views

backpropagation: why find the global minimum instead of the value of zero

in back propagation, you use gradient descent to find the stationary point on the equation of the Error = (in terms of weight). But don't we want the error to be equal to zero? if the error is zero, ...
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1answer
107 views

Gini index on data with error margins

I have data series and I want to calculate Gini coefficients for each row as an estimate of matrix sparsity. Hoever values contained in the rows are not exact and have error bounds. My question is ...
3
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2answers
2k views

Error propagation and Standard Deviation

I never quite got the hang of this during my entry stat course and it has been bugging me for a long time now. Lets assume I'm trying to find the focal length of a concave lens. Using a mockup ...
3
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0answers
1k views

Propagation of uncertainty (intersection of two graphs)

The situation is as follows: I performed necessary measurements and used them to create two graphs. I used polynomial regression to find the point of intersection. What I know: precision of ...